Electrons pairing against all odds

Superconductivity is an astonishing phenomena. Besides its obvious practical implications; e.g. carrying electrical current without resistance or generating huge magnetic fields, it is also the fertile ground on which fundamental and non-trivial physics manifests itself. Examples are vortex matter, topological phase transitions and the Higgsing of the photon. However, the properties of the superconducting phase itself are not the only fascinating part of the story. In order to become superconducting, the electrons in the parent metal  need to form bound states called "Cooper pairs." But here lies a conundrum; how do two particles with the same electrical charge form a bound state?  In this talk I will discuss the formation process of these pairs. I will first discuss the canonical understanding of this process and explain how we derive a quantum field theory for such superconductors. I will then show that there are many superconducting materials that challenge this theory. (Namely, according to existing theory these superconductors are not supposed to be; they are dubbed "unconventional superconductors.") I will then conclude by presenting an alternative theory we have developed to explain Cooper pairing of massless Dirac electrons at their "Charge neutrality" point with the aid of a "quantum critical point."